# Copyright 2017-2020 The GPflow Contributors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import Any, Callable, Optional, Type, Union, cast
import numpy as np
import tensorflow as tf
from .. import kernels
from .. import mean_functions as mfn
from ..base import TensorType
from ..covariances import Kuf
from ..inducing_variables import InducingVariables
from ..probability_distributions import DiagonalGaussian, Gaussian, MarkovGaussian
from ..quadrature import mvnquad
from . import dispatch
from .expectations import ExpectationObject, PackedExpectationObject, quadrature_expectation
register = dispatch.quadrature_expectation.register
NoneType: Type[None] = type(None)
EllipsisType = Any
[docs]def get_eval_func(
obj: ExpectationObject,
inducing_variable: Optional[InducingVariables],
slice: Union[slice, EllipsisType, None] = None,
) -> Callable[[TensorType], tf.Tensor]:
"""
Return the function of interest (kernel or mean) for the expectation
depending on the type of :obj: and whether any inducing are given
"""
slice = ... if slice is None else slice
if inducing_variable is not None:
# kernel + inducing_variable combination
if not isinstance(inducing_variable, InducingVariables) or not isinstance(
obj, kernels.Kernel
):
raise TypeError("If `inducing_variable` is supplied, `obj` must be a kernel.")
return lambda x: tf.transpose(Kuf(inducing_variable, obj, x))[slice]
elif isinstance(obj, mfn.MeanFunction):
return lambda x: obj(x)[slice] # type: ignore
elif isinstance(obj, kernels.Kernel):
return lambda x: obj(x, full_cov=False) # type: ignore
raise NotImplementedError()
@dispatch.quadrature_expectation.register(
(Gaussian, DiagonalGaussian),
object,
(InducingVariables, NoneType),
object,
(InducingVariables, NoneType),
)
def _quadrature_expectation_gaussian(
p: Union[Gaussian, DiagonalGaussian],
obj1: ExpectationObject,
inducing_variable1: Optional[InducingVariables],
obj2: ExpectationObject,
inducing_variable2: Optional[InducingVariables],
nghp: Optional[int] = None,
) -> tf.Tensor:
"""
General handling of quadrature expectations for Gaussians and DiagonalGaussians
Fallback method for missing analytic expectations
"""
nghp = 100 if nghp is None else nghp
# logger.warning(
# "Quadrature is used to calculate the expectation. This means that "
# "an analytical implementations is not available for the given combination."
# )
if obj1 is None:
raise NotImplementedError("First object cannot be None.")
if not isinstance(p, DiagonalGaussian):
cov = p.cov
else:
if (
isinstance(obj1, kernels.Kernel)
and isinstance(obj2, kernels.Kernel)
and obj1.on_separate_dims(obj2)
): # no joint expectations required
eKxz1 = quadrature_expectation(
p, cast(PackedExpectationObject, (obj1, inducing_variable1)), nghp=nghp
)
eKxz2 = quadrature_expectation(
p, cast(PackedExpectationObject, (obj2, inducing_variable2)), nghp=nghp
)
return eKxz1[:, :, None] * eKxz2[:, None, :]
cov = tf.linalg.diag(p.cov)
if obj2 is None:
def eval_func(x: TensorType) -> tf.Tensor:
fn = get_eval_func(obj1, inducing_variable1)
return fn(x)
else:
def eval_func(x: TensorType) -> tf.Tensor:
fn1 = get_eval_func(obj1, inducing_variable1, np.s_[:, :, None])
fn2 = get_eval_func(obj2, inducing_variable2, np.s_[:, None, :])
return fn1(x) * fn2(x)
return mvnquad(eval_func, p.mu, cov, nghp)
@dispatch.quadrature_expectation.register(
MarkovGaussian, object, (InducingVariables, NoneType), object, (InducingVariables, NoneType)
)
def _quadrature_expectation_markov(
p: MarkovGaussian,
obj1: ExpectationObject,
inducing_variable1: Optional[InducingVariables],
obj2: ExpectationObject,
inducing_variable2: Optional[InducingVariables],
nghp: Optional[int] = None,
) -> tf.Tensor:
"""
Handling of quadrature expectations for Markov Gaussians (useful for time series)
Fallback method for missing analytic expectations wrt Markov Gaussians
Nota Bene: obj1 is always associated with x_n, whereas obj2 always with x_{n+1}
if one requires e.g. <x_{n+1} K_{x_n, Z}>_p(x_{n:n+1}), compute the
transpose and then transpose the result of the expectation
"""
nghp = 40 if nghp is None else nghp
# logger.warning(
# "Quadrature is used to calculate the expectation. This means that "
# "an analytical implementations is not available for the given combination."
# )
if obj2 is None:
def eval_func(x: TensorType) -> tf.Tensor:
return get_eval_func(obj1, inducing_variable1)(x)
mu, cov = p.mu[:-1], p.cov[0, :-1] # cross covariances are not needed
elif obj1 is None:
def eval_func(x: TensorType) -> tf.Tensor:
return get_eval_func(obj2, inducing_variable2)(x)
mu, cov = p.mu[1:], p.cov[0, 1:] # cross covariances are not needed
else:
def eval_func(x: TensorType) -> tf.Tensor:
x1 = tf.split(x, 2, 1)[0]
x2 = tf.split(x, 2, 1)[1]
res1 = get_eval_func(obj1, inducing_variable1, np.s_[:, :, None])(x1)
res2 = get_eval_func(obj2, inducing_variable2, np.s_[:, None, :])(x2)
return res1 * res2
mu = tf.concat((p.mu[:-1, :], p.mu[1:, :]), 1) # Nx2D
cov_top = tf.concat((p.cov[0, :-1, :, :], p.cov[1, :-1, :, :]), 2) # NxDx2D
cov_bottom = tf.concat((tf.linalg.adjoint(p.cov[1, :-1, :, :]), p.cov[0, 1:, :, :]), 2)
cov = tf.concat((cov_top, cov_bottom), 1) # Nx2Dx2D
return mvnquad(eval_func, mu, cov, nghp)